Min Time Problem Homework: A to B in Min Time

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Homework Help Overview

The problem involves calculating the minimum time required for a car to travel from point A to point B, where B is positioned at a distance of 120 km down the road and 75 km perpendicular to it. The car has different speeds on and off the road, specifically 100 km/h on the road and 50 km/h off the road.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the geometric setup of the problem, including the relationship between points A and B. Questions are raised about the clarity of the problem statement and the necessary information regarding speed. Some suggest a method involving the calculation of distances and times based on a variable distance L along the road.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem's setup and exploring different approaches to formulate the time minimization function. There is no explicit consensus yet, but some productive lines of reasoning have been proposed regarding the relationship between the distances traveled and the corresponding times.

Contextual Notes

There are indications of missing information or unclear definitions in the problem statement, particularly regarding the reference points for distances and the speeds involved. Participants are actively questioning these assumptions.

bondgirl007
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Homework Statement



A straight road runs through A. B is 120 km down from the road and 75 km perpendicular to the road. A car travels 100 km/h on road and 50 km/h off road. Find the minimum time required to travel from A to B.

Homework Equations


The Attempt at a Solution



I'm not sure how to start this equation. I have drawn a triangle but not sure what to do next. Any help would be greatly appreciated!
 
Last edited:
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What you have said make pretty much no sense!

"A straight road runs through A. B is 120 km down and 75 km perpendicular." B is 120 km down from what? and 75 km perpencular to what?

Oh, and "minimum time" required to drive any distance requires that we know some speed! What information are you not telling us?
 
I edited my question.

I did have speed in it.
 
If I've understood correctly, I can get from A to B by going 120 km along a road, and then going perpendicular to the road for 75 km.

Suppose I go a distance L along the road, and then head offroad at an angle towards B.

1) What is the distance to B from the point where I leave the road?

2) What is the total time I travel on the road? What is the total time I travel off the road?

Add these two. You now have a function of L. Minimize with respect to L.
 

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